Some stem browning out in the Fall is normal as the plants harden and prepare for winter but Lord, the stems should not be falling down if it is that. I would first check the soil moisture and inspect the length of the stem -including the area where it connects to the base/crown- looking for signs of "damage" by insects (not likely but always worth a shot).

The alternatives are difficult to identify without technical help. Root rot can make the stems loose color as the roots decay and then the stem browns out albeit root rot tend to a-l-s-o cause leaf issues like wilting, which you do not report. Odd that root rot would not cause leaf symtoms. Note that if it is root rot, leaf wilt may happen once the stem browns out near/around the leaf's petiole. A non scientific test for root rot is to see if the soil is wet for long periods & to extract the plant and check the roots, even smell the roots. You can do that to one of the worst ones since pulling it out will affect the look of the hedge so think about whether you want to do that or take it for analysis instead. See the info on Phytophthora Root Rot below:

http://www.aces.edu/pubs/docs/A/ANR-1212/index2.tmpl

Another fungi called corniespora (Sp?) can cause stem rot in hydrangeas, albeit very rarely and it tends to make leaves wilt too. There are fungicides recommended but I am not sure if this is your issue since your notes did not mention leaf wilt.

Bacterial pathogens like pseudonomas can cause either leaf spots and-or stem rots on hydrangeas. There is no easy way to diagnose psedunomas as Agric Extension Folks are the ones who have the equipment to detect/identify it. The usual clean sanitation practices are recommended as well as the destruction of infected plants and use of copper fungicides.

So, I suggest a quick trip to the nearest Agric Extension Office with a sample in a tightly sealed transparent bag since this is spreading so fast.